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University of Groningen
Kinetics, selectivity and scale up of the Fischer-Tropsch synthesisvan der Laan, Gerard Pieter
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Publication date:1999
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Abstract
Thekineticsof thegas-solidFischer-Tropschsynthesisover a commercialFe-Cu-K-SiO2 catalystwasstudiedin a continuousspinningbasket reactor. Experimentalcon-ditionswerevariedasfollows: reactorpressureof 0.8-4.0MPa, H2/CO feedratio of0.25-4.0,andspacevelocityof 0.5-2.010¶ 3 Nm3 kg¶ 1
cat s¶ 1 ataconstanttemperatureof523K. A numberof rateequationswerederivedonthebasisof adetailedsetof possi-ble reactionmechanismsoriginatingfrom thecarbidemechanismfor thehydrocarbonformationandtheformatemechanismfor thewatergasshift reaction,respectively. 14modelsfor theFischer-Tropschreactionrateand2 watergasshift reactionratemodelswerefitted to theexperimentalreactionrates.Bartlett’s testwasusedto reducethesetof Fischer-Tropschrateequationsto 3 models,which werestatisticallyindistinguish-able. It couldbeconcludedthat the reactionrateof theFischer-Tropschsynthesisiscontrolledby the formationof the monomerspecies(methylene)by hydrogenationof molecularlyadsorbedCO, whereasthe carbondioxide formationrate (watergasshift) is determinedby theformationof a formateintermediatespeciesfrom adsorbedCO anddissociatedhydrogen.Simulationsusingtheoptimalkinetic modelsderivedshowed goodagreementboth with experimentaldataandwith somekinetic modelsfrom literature.
145
146 CHAPTER 5
5.1 Intr oduction
TheFischer-Tropschsynthesiscanbesimplifiedasa combinationof theFT reactionandthewatergasshift (WGS)reaction.Wateris aprimaryproductof theFT reaction,andCO2 canonly be producedby the WGS reaction(RWGS · RCO2). The watergasshift reactionis a reversibleparallel-consecutivereactionwith respectto CO (seeFigure5.1).
CO + H2 H2O + -(CH2)-
CO + H2O
+CO2
RFT
RWGS
Figure5.1 Schemeof thereactionof carbonmonoxideandhydrogen.
Themajorproblemin describingFischer-Tropschreactionkineticsis thecomplex-ity of its reactionmechanismandthelargenumberof speciesinvolved. Literatureonthe kineticsof the Fischer-Tropschsynthesiscanbe divided into two classes.Moststudiesaimatcatalystimprovementandpostulateempiricalpowerlaw kineticsfor thecarbonmonoxiderates[1, 2]:
¸ RCO · k PaH2
PbCO (5.1)
andcarbondioxideformationor watergasshift reaction[3, 4]:
RCO2 · k PcH2O Pd
CO (5.2)
Relatively few studiesaim at understandingthereactionmechanisms.Someauthorsderived Langmuir-Hinshelwood- Hougen-Watson(LHHW) rate expressionsfor thereactantconsumption[5, 6]. In mostcasestheratedeterminingstepwasassumedtobetheformationof thebuilding block or monomer, methylene[7–14]. Simultaneousmodelingof theWGSandFT reactionsoniron catalystswith WGSactivity hashardlybeenreported.ZimmermanandBukur [9] andShenet al. [15] fitted kinetic expres-sionsto theirdata,but their rateexpressionsfor theWGSwerelargelyempirical.
Our objective is to develop intrinsic rate expressionsfor the CO conversiontoFischer-Tropschproductsandfor the watergasshift (WGS) reactionover a precip-
INTRINSIC K INETICS OF THE GAS-SOLID FT AND WGS REACTIONS 147
itated iron catalyston the basisof realisticmechanisms.It alsoappearedthat sev-eral existing literaturemodelscan be derived from the samelimited set of mecha-nisms[7–14]. A reactormodel will be usedto predict the reactionratesand con-versionsasa functionof experimentalconditions.Comparisonbetweenthenew rateexpressionsandavailable literaturemodelsis includedaswell. The kineticsof thegas-solidFischer-Tropschsynthesisover a commercialFe-Cu-K-SiO2 catalystwerestudiedin a continuousspinningbasket reactor(CSTR)at industrially relevant con-ditions. Productdistributionsat thesamereactionconditionsarereportedin Chapter4.
5.2 Theory
5.2.1 ActiveSiteson Precipitated Ir on Catalysts
The compositionof iron-basedcatalystschangesduring Fischer-Tropschsynthesis.ZhangandSchrader[16] concludedthat two active sitesoperatesimultaneouslyonthe surfaceof iron catalysts:Fe0/Fe-carbidesand magnetite(Fe3O4). The carbidephaseis active towardsdissociationof CO andformationof hydrocarbons,while theoxidephaseadsorbsCO associatively andproducespredominantlyoxygenatedprod-ucts. Lox et al. [17] andShroff et al. [18] concludedthat the magnetitephasehasnegligible catalyticactivity towardsFT reactionswhereascarbideformationresultsinahighFT activity.
Severalauthorsproposedthatmagnetite(Fe3O4) is themostactive phasefor theWGS reaction[4, 5, 16, 19, 20] on iron catalysts. Raoet al. [19] studiedthe ironphaseof Fe/Cu/K/SiO2 catalystsfrom thedemonstrationunit at LaPorte,Texas(Au-gust,1992)with Mossbauerspectroscopy. Thechangesof themagnetitephasecorre-spondedwith theWGSreactionactivity duringtime-on-stream.Lox etal. [17] showedthatFe3O4 coexistswith variousiron carbideson thecatalystduringsynthesisgasre-actions.It is generallyacceptedthat theWGSandFT reactionsproceedon differentactivesitesonprecipitatediron catalysts[5, 19].
5.2.2 Hydr ocarbonFormation
5.2.2.1 Elementary Reactions
Themechanismof thehydrocarbonformationduringtheFTShasbeenreviewedanddiscussedby severalauthors[1, 21–24]. Recentreviews weregivenby Hindermannetal. [25], Dry [26], Dry [27], andAdesina[28] andin Chapter2. Themostimportant
148 CHAPTER 5
growthmechanismfor thehydrocarbonformationis thesurfacecarbidemechanismbyCH2 insertion[1, 6, 29,30]. Thepresenceof adsorbedmethylenehasbeenidentifiedwith isotopic-tracertechniquesonFe/Al2O3 [31].
The formationof the methylenespecieswill be discussedin more detail. Hy-drogenreactsvia eitherthedissociative adsorbedstateor in themolecularstate[32].Dissociativeadsorptionof hydrogenproceedson two freeactivesites:
H2 ¹ 2s1 º » 2Hs1 (5.3)
s1 denotesa catalyticsitewherehydrocarbonscanbeformed. Carbonmonoxidead-sorbsassociatively onanactivesite[32]:
CO ¹ s1 º » COs1 (5.4)
AdsorbedCOcanbedissociatedin asecondstep:
COs1 ¹ s1 º » Cs1 ¹ Os1 (5.5)
Surfacecarbonreactswith adsorbeddissociatedhydrogen,
Cs1 ¹ Hs1 º » CHs1 ¹ s1 (5.6)
CHs1 ¹ Hs1 º » CH2s1 ¹ s1 (5.7)
or with molecularhydrogen,
Cs1 ¹ H2 º » CH2s1 (5.8)
Oxygenis removed irreversibly andrapidly from the surfaceby consecutive hydro-genationreactions[24, 33,34],
Os1 ¹ Hs1 º HOs1 ¹ s1 (5.9)
HOs1 ¹ Hs1 º H2Os1 ¹ s1 (5.10)
H2Os1 º » H2O ¹ s1 (5.11)
or with molecularhydrogenaccordingto anEley-Ridealmechanism[8, 24,33],
Os1 ¹ H2 º H2Os1 (5.12)
H2Os1 º » H2O ¹ s1 (5.13)
INTRINSIC K INETICS OF THE GAS-SOLID FT AND WGS REACTIONS 149
Anotherpossiblemechanismstartswith molecularlyadsorbedcarbonmonoxideandsuccessivehydrogenassisteddissociationwith dissociatedhydrogen[6, 8],
COs1 ¹ Hs1 º » HCOs1 ¹ s1 (5.14)
HCOs1 ¹ Hs1 º » Cs1 ¹ H2Os1 (5.15)
or molecularhydrogen,
COs1 ¹ H2 º » HCOHs1 ¹ s1 (5.16)
HCOHs1 ¹ H2 º » CH2s1 ¹ H2O (5.17)
Basedon theseelementaryreactions,we definedfour differentpossiblemecha-nisms.SeeTable5.1 for theconventionsandstateof thereactantsin theelementaryformationreactionsof methylene.Thecompletesetof elementaryreactionsfor eachmodelis givenin Table5.2.
Table5.1 Thevariouskineticmodelsconsidered,togetherwith thepresenceof thereactantsin theratedeterminingstep.Model CO H2
FT-I Dissociative DissociativeFT-II Dissociative MolecularFT-III Associative DissociativeFT-IV Associative Molecular
5.2.2.2 Kinetic RateEquations
In orderto deriverateequations,weusedtheLangmuir-Hinshelwood-Hougen-Watsonapproach,see,for example,Graafet al. [35]. For eachmodel,the possibleratede-terminingstepswere identified,while all otherstepswereassumedto be at quasi-equilibrium. The following assumptions,all basedon literature,weretaken into ac-count:
1. Reactionpathfor the CO consumptionto the monomermethylene,CH2, con-tainsoneirreversibleratedeterminingstep,in analogywith Ref. [35].
2. Steadystateconcentrationsof all intermediateson thecatalystsurface[35, 36].
150 CHAPTER 5
Table5.2 Elementaryreactionsfor FT synthesis.Model Number Elementaryreaction
FT-I 1 CO+ s1 º » COs1
2 COs1 + s1 º » Cs1 + Os1
3 Cs1 + Hs1 º » CHs1 + s1
4 CHs1 + Hs1 º » CH2s1+ s1
5 Os1 + Hs1 º HOs1 + s1
6 HOs1 + Hs1 º H2Os1 + s1
7 H2O + s1 º » H2Os1
8 H2 + 2s1 º » 2Hs1
FT-II 1 CO+ s1 º » COs1
2 COs1 + s1 º » Cs1 + Os1
3 Cs1 + H2 º » CH2s1
4 Os1 + H2 º H2Os1
5 H2O + s1 º » H2Os1
FT-III 1 CO+ s1 º » COs1
2 COs1 + Hs1 º » HCOs1 + s1
3 HCOs1 + Hs1 º » Cs1 + H2Os1
4 Cs1 + Hs1 º » CHs1 + s1
5 CHs1 + Hs1 º » CH2s1 + s1
6 H2 + 2s1 º » 2Hs1
7 H2O + s1 º » H2Os1
FT-IV 1 CO+ s1 º » COs1
2 COs1 + H2 º » H2COs1
3 H2COs1 + H2 º » CH2s1 + H2O
4 H2O + s1 º » H2Os1
1Equilibriumconstant,e.g.reactionstepFT-I1: K1 ¼ ½ COs1
PCO ½ s1
INTRINSIC K INETICS OF THE GAS-SOLID FT AND WGS REACTIONS 151
Table5.3 ReactionrateexpressionsconsideredfortheFischer-Tropschsynthesis,RFT (mol kg¶ 1
cat s¶ 1).
Model Kinetic equation
FT-I3kP1¾ 2
CO P1¾ 2H2
1 ¹ aP1¾ 2CO ¹ bPH2O
2
FT-I4kP1¾ 2
CO P3¾ 4H2
1 ¹ aP1¾ 2CO P ¶ 1¾ 4
H2 ¹ bPH2O
2
FT-II3kP1¾ 2
CO PH2
1 ¹ aP1¾ 2CO ¹ bPH2O
FT-III2kPCO P1¾ 2
H2
1 ¹ aPCO ¹ bPH2O2
FT-III3kPCO PH2
1 ¹ aPCO ¹ bPH2O2
FT-IV2kPCO PH2
1 ¹ aPCO ¹ bPH2O
FT-IV3kPCO P2
H2
1 ¹ aPCO ¹ bPH2O
3. Catalystsitesof type 1 areactive towardshydrocarbonformation,which areuniformandhomogeneouslydistributed[35, 36].
4. Initial adsorptionof hydrogenandcarbonmonoxideis in quasi-equilibriumwiththegasphaseconcentrations[24].
5. Wateris removedirreversiblyafterCOdissociation[24, 33,37].
6. CO is adsorbedmore strongly than H2 on iron catalysts,resultingin a highsurfaceconcentrationof COor dissociatedCOrelative to H2 [21, 38].
7. H2O adsorbsstronglyandmayinhibit theFT reactionrate[9].
With theseassumptions,7 differentkinetic modelsremainpossible. Thesearesummarizedin Table5.3. Thedevelopmentof thekineticequationswill beillustratedfor modelFT-II3. The modelcodesrefer to the setof elementaryreactionsandtheelementaryreactionnotatequilibrium(thatis theratedeterminingstep,soin thiscase
152 CHAPTER 5
Table5.4 Parametersfor theFT kineticmodels.Model k (x) a (x) b
(mol kg¶ 1 s¶ 1 MPax) (MPax) (MPa¶ 1)FT-I3 ¿ k3k5K1K2K8 À 1¾ 2 (-1) ¿ K1K2k5Á k3 À 1¾ 2 (-1/2) K7
FT-I4 ¿ k4k5K1K2K3 À 1¾ 2K 3¾ 48 (-5/4) ¿ K1K2K3K 1¾ 2
8 k5Á k4 À 1¾ 2 (-1/4) K7
FT-II3 ¿ k3k4K1K2 À 1¾ 2 (-3/2) ¿ k4K1K2 Á k3 À 1¾ 2 (-1/2) K5
FT-III2 k2K1K 1¾ 26 (-3/2) K1 (-1) K7
FT-III3 k3K1K2K6 (-2) K1 (-1) K7
FT-IV2 k2K1 (-2) K1 (-1) K4
FT-IV3 k3K1K2 (-3) K1 (-1) K4
reaction3). Thesetof elementaryreactionsfor modelFT-II3 is shown in Table5.2.Thereactionrateof theratedeterminingstepis:
RFT-II3 · k3Â Cs1 PH2 · k4 Â Os1 PH2 (mol kg¶ 1cat s¶ 1) (5.18)
Thesurfacefractionof carboncanbecalculatedfrom thesitebalance,theprecedingreactionstepswhichareatquasi-equilibriumandthereactionratefor waterformation:
K1 · Â COs1
PCO Â s1 Ã K2 · Â Cs1 Â Os1Â COs1 Â s1
(5.19)
 Cs1 · k4
k3Â Os1 · K1K2k4
k3
1¾ 2P1¾ 2
CO Â s1 (5.20)
Fromassumptions6 and7 it follows thatonly surfacecarbonandwateroccupy asignificantfractionof thetotalnumberof sites,thesitebalancebecomes:
 s1 ¹Ä Cs1 ¹Ä H2Os1 · 1 (5.21)
Substitutionof thesurfacefractionof carbonin eq5.18:
RFT-II3 · Å k3k4K1K2 Æ 1¾ 2P1¾ 2CO PH2
1 ¹ Å K1K2k4Ç k3 Æ 1¾ 2P1¾ 2CO ¹ K5PH2O
· kP1¾ 2CO PH2
1 ¹ aP1¾ 2CO ¹ bPH2O
(5.22)
Table5.3summarizesthefinal form of thevariousrateexpressionsfor the7 pos-siblekinetic modelsconsidered,whereasTable5.4 shows thekinetic andadsorptionparametersfor thedifferentkineticmodels.It canbeseenthatthepressuredependencyof COandH2 in thenumeratorrangesfrom 1/2to 1,and1/2to 2, respectively. Thede-nominatoris quadraticin caseof adualsiteelementaryreaction,in contrastto asingle
INTRINSIC K INETICS OF THE GAS-SOLID FT AND WGS REACTIONS 153
siteratedeterminingstep.Thedenominatorconsistsof theindividualcontributionsofsignificantlyabundantspecieson thecatalystsurface.
Theconcentrationof freesites s1 is determinedfrom asitebalance.It is assumedthatthetotalnumberof sitesis constant:
 s1 ¹ n
i È 1Â i s1 · 1 (5.23)
where  s1 is the fraction free sitesand  i s1 are the surfacefractionsoccupiedwithadsorbedspeciessuchas carbon,carbonmonoxide,hydrogen,alkyl chains,water,carbondioxide,andsoforth Theadditionof severalinhibition termsin thedenomina-tor cannot be justifiedstatisticallydueto a high degreeof covarianceor correlation[39, 40]. The derived kinetic expressionshave a maximumof two inhibition terms:onetermfor COor acarbidicspecies(  Cs1) andtheotherfor H2O inhibition.
5.2.2.3 Literatur eModels
Reviewsof kineticequationsfor iron-basedcatalystswerepublishedby Huff andSat-terfield [8], ZimmermanandBukur [9], andVan der LaanandBeenackers[45], en-closedin slightly revisedform asChapter2. Kinetic studiesof theFTSon iron andcobaltcatalystsaresummarizedin Table5.5.Thecorrespondingoperatingconditionsaregivenin Chapter2 (Table2.7).
It canbeshown thatall theseliteraturemodelscanbederivedfromthesetof mech-anismsconsideredin this studyandwhich aresummarizedin Table5.2. Appropriateassumptionsfor theinhibitor effectsin thesitebalanceof thekinetic rateexpressionsin table5.3 resultin similar mathematicalexpressions.Themechanisticimplicationsof theavailableFT kineticmodelsaresummarizedin Table5.5.
5.2.3 Water GasShift Reaction
5.2.3.1 ReactionMechanism
Several mechanismsfor the watergasshift reactionwereproposedin the literature.Singlestudiesof the watergasshift reactionover supportedmetalssuggestthe ap-pearanceof formatespecies[4, 5, 20,35]. Theformatespeciescanbeformedby thereactionbetweeneitherahydroxyspeciesor waterandcarbonmonoxideeitherin thegasphaseor in the adsorbedstate. The hydroxy intermediatecanbe formedby thedecompositionof water. Theformateintermediatecanbereducedto eitheradsorbedor gaseouscarbondioxide (seeTable5.6). RethwischandDumesic[20] studiedthewater gasshift reactionon several supportedand unsupportediron oxide and zinc
154 CHAPTER 5
Table5.5 Reactionrateequationsoverallsynthesisgasconsumptionrate.SeeTable2.7forexperimentalconditions,reactortypeandcatalystapplied.
Kinetic expression References Mechanisticimplications
(a) kPH2 [9, 22,41] FT-II3 (b=0,aPCO É 1)FT-IV2 (b=0,aPCO É 1)
(b) kPaH2
PbCO [3] -
(c)kPH2 PCO
PCO ¹ K PH2O[7, 9, 10,15,22] FT-IV2 (aPCO andbPH2OÉ 1)
(d)kP2
H2PCO
PCO PH2 ¹ K PH2O[8, 15,42,43] FT-II3 (waterformationis
reversible)
(e)kP2
H2PCO
1 ¹ aPCO P2H2
[22] -
(f)kPH2 PCO
PCO ¹ K PCO2
[9, 11,12,43] FT-IV2 (aPCO É 1 andCO2 inhibition)
(g)kPH2 PCO
PCO ¹ K1PH2O ¹ K2PCO2
[9, 11,12] FT-IV2 (aPCO É 1, CO2
andH2O inhibition)
(h)kP1¾ 2
CO P1¾ 2H2
1 ¹ K1P1¾ 2CO ¹ K2P1¾ 2
H2
2 [14] FT-I3 (H2 inhibition,bPH2O · 0)
(i)kPCO P1¾ 2
H2
1 ¹ K1PCO ¹ K2P1¾ 2H2
2 [6] FT-III2 (H2 inhibition,bPH2O · 0)
(j)kPCO PH2
Å 1 ¹ K PCO Æ 2 [13, 40,44] FT-III3 (bPH2O · 0)
INTRINSIC K INETICS OF THE GAS-SOLID FT AND WGS REACTIONS 155
Table5.6 Elementaryreactionsfor thewatergasshift reaction.Model Number Elementaryreaction
WGS-I 1 CO+ s2 º » COs2
2 CO2 + s2 º » CO2s2
3 H2O + s2 º » H2Os2
4 H2 + 2s2 º » 2Hs2
5 COs2 + H2Os2 º » HCOOs2 + Hs2
6 HCOOs2 + s2 º » Hs2+ CO2s2
WGS-II 1 CO+ s2 º » COs2
2 CO2 + s2 º » CO2s2
3 H2O + s2 º » H2Os2
4 H2Os2 + s2 º » OHs2 + Hs2
5 H2 + 2s2 º » 2Hs2
6 COs2 + OHs2 º » HCOOs2 + s2
7 HCOOs2 + s2 º » Hs2+ CO2s2
oxide catalysts.They suggestedthat the WGS reactionover unsupportedmagnetiteproceedsvia a directoxidationmechanism,while all supportediron catalystsoperatevia a mechanismwith formatespeciesdueto limited changeof oxidationstateof theiron cations.
5.2.3.2 Kinetic Expressions
Severalassumptionsweremadein orderto derive theLHHW rateexpressions:
Ê Steadystatefor theadsorbedspecies.
Ê Oneratedeterminingstepin thesequenceof elementaryreactionsoverthecom-pleterangeof experimentalconditions.
Ê Surfaceconcentrationsof intermediatespeciesarenegligible [35].
Ê Activesitesfor theWGS(type2) aredifferentthanthesitesfor thehydrocarbonforming reactions(type1) [5].
156 CHAPTER 5
Ê Ratedeterminingstepis a dual-siteelementaryreactionbetweentwo adsorbedspecies[5].
Ê Adsorptionof reactantsanddesorptionof productsareatequilibrium.
With the mentionedassumptionstwo ratedeterminingstepsarepossible. First, theratedeterminingstepis (WGS-II6):
COs2 ¹ OHs2 º » HCOOs2 ¹ s2 (5.24)
Thehydroxylspeciesis formedby dissociationof water:
H2O ¹ 2s2 º » OHs2 ¹ Hs2 (5.25)
Second,thereactionbetweenadsorbedwaterandcarbonmonoxide(WGS-I5)canberatedetermining:
COs2 ¹ H2Os2 º » HCOOs2 ¹ Hs2 (5.26)
On basisof the formatemechanismandthe mentionedassumptions,two kineticrateequationsweredeveloped.Theexpressionsaregivenin Table5.7.Theadsorptionof H2 andCO2 areassumedto benegligible relative to CO andH2O [5, 9, 38]. Thus,themassbalanceof thecatalyticsites,s2, is:
 s2 ¹Ä H2Os2 ¹Ä COs2 · 1 (5.27)
Derivation of otherkinetic expressionsbasedon adsorptionof morecomponentsispossiblefrom theaboveequations.SincetheWGSreactionis anequilibriumreaction,thereversereactionhasto betakeninto account.For the temperaturedependency ofthe equilibrium constantof the WGS reaction,K P, the following relationwasused(Graafet al. [46]):
log K P · logPCO2 PH2
PH2O PCO eq· 2073
T¸ 2 Ë 029 (5.28)
Kinetic studiesof theWGSreactionunderFT conditionson iron-basedcatalystsaresummarizedin Chapter2 (Table2.8).
INTRINSIC K INETICS OF THE GAS-SOLID FT AND WGS REACTIONS 157
Table5.7 Rateexpressionsconsideredfor thewatergasshift reaction,RCO2 (mol kg¶ 1
cat s¶ 1).
Model Kinetic equation Sitebalance
WGS-I5kÌ PCO PH2O
¸ PCO2 PH2 Ç K P
1 ¹ K1PCO ¹ K3PH2O2 s2, COs2, H2Os2
kÌ = k5K1K3 (mol kg¶ 1 s¶ 1 MPa¶ 2)
WGS-II6kÌ PCO PH2O Ç P1¾ 2
H2¸ PCO2 P1¾ 2
H2 Ç K P
1 ¹ K1PCO ¹ K3PH2O2 s2, COs2, H2Os2
kÌ = k5K1K3K4K ¶ 1¾ 25 (mol kg¶ 1 s¶ 1 MPa¶ 1Í 5)
5.3 Experimental
The kineticsof both the Fischer-Tropschsynthesisand the watergasshift reactionover a commercialprecipitatediron catalyst(RuhrchemieLP33/81)wereunraveledby relevantexperimentsin a SpinningBasket Reactor(SBR).For a detaileddescrip-tion of theexperimentalset-up,thecatalystapplied,theanalyticandtheexperimentalprocedures,seeChapter3.
Thebasketswereloadedwith 2.34g of catalyst,with particlediametersbetween0.125and0.160mm. Thecatalystwaspretreatedwith a hydrogenflow rateof 8.3310¶ 4 Nm3 kg¶ 1
cat s¶ 1 accordingto Bukur et al. [47]. Thereactortemperaturewaslin-early increasedfrom 293 to 553K by 0.017K /s. The reactortemperaturewaskeptat 553 K for 24 hrs at atmosphericpressure.After catalystreduction,synthesisgaswas fed to the reactorwhich at standardconditionsoperatedat 523 K, 1.50 MPa,(H2/CO)f eed=2 andaspacevelocityof 1.5110¶ 3 Nm3 kg¶ 1
cat s¶ 1.
Checkingthecriteriaof WeiszandPrater[48] for thereactantsCOandH2 showedthatnointraparticlediffusionlimitationsoccurredatrelevantexperimentalconditions,evennot at thehighestconversionrates.Here,it wasconservatively assumedthatthecatalystporeswerefilled with long-chainhydrocarbonwaxes.
24 kinetic experimentswerecarriedout in theSBRwith theRuhrchemieprecipi-tatediron catalyst.Theexperimentalconditionswerevariedasfollows: P= 0.8 - 4.0MPa,H2/COfeedratio=0.25- 4.0,and Î i nÏ$Ð 0Ç W= 0.510¶ 3 - 2.010¶ 3 Nm3 kg¶ 1
cat s¶ 1 ata temperatureof 523K. At regularintervals,thestandardexperimentwasrepeatedto
158 CHAPTER 5
determinepossibledeactivationeffectsof thecatalyst.A summaryof theexperimentalresultsandoperatingconditionsis givenin AppendixA.
5.4 Resultsand Discussion
After an initial periodof 100hrs,a steadystatewasmoreor lessobtained.Thecat-alyst activity, reactionrateto hydrocarbonproducts(RFT ) andthe rateof the watergasshift (RWGS) did not changemuchover 1200hrs time on stream(seeChapter3;Figure3.10a).Thereactionrateswerenotcorrectedfor catalystagingdueto thesmalleffectof timeonstreamon thecatalystactivity.
The preliminary screeningof the Fischer-Tropschkinetic expressionswas per-formedwith a maximumof two adsorbedspeciesin the site balance.Every kineticmodelwasoptimizedwith two differentmathematicalformsof thesitebalance:
 s1 ¹ Å Â Cs1 or  COs1 Æ ¹Ä H2Os1 · 1 (5.29)
Å Â Cs1 or  COs1 Æ ¹Ä H2Os1 · 1 (5.30)
For modelsbasedon thecarbidemechanism(FT-I, FT-II), thecarbidicspeciesis sur-facecarbon Cs1, formedby dissociationof CO.ModelsFT-III andFT-IV arebasedonassociative adsorbedCO species COs1. The7 kinetic equationswereoptimizedwitha non-linearoptimizationroutineusingboth eqs5.29 and5.30 for the site balance.Contributionsof speciesin the site balancewereeliminatedif the fitted adsorptioncoefficientswerenot significantlydifferentfrom zeroor hada significantlynegativevalue.Table5.8shows theresultsof thekineticmodelswith therelativevarianceandtheirranking.Fourmodelsareableto describetheexperimentalFT reactionrateswitha relativevariancelessthan35% andamaximumof threeoptimizedparameters.
Bartlett’s testwasappliedto investigatewhetherthedifferencesin accuracy of thevariousmodelswerestatisticallysignificant[49, 50]. This test comparesa criticalcalculatedÑ 2
c value(for details,seeChapter3 or Jonker et al. [49]) with a tabulatedÑ 2t value[51]. If Ñ 2
c exceedsthetabulatedvalue,themodelwith thelargestdeviationwasrejectedand Ñ 2
c wasrecalculated.Modelsweresubsequentlyrejected,until Ñ 2c
wasbelow thetabulatedvalue.Table5.9comparesÑ 2c with thetabulatedÑ 2
t valueforH ¸ 1 degreesof freedom.Thetableshows thatthebestfivemodels(H · 5) passedthetestandarestatisticallyindistinguishable.Thebestfivemodelsare,in succeedingorder: FT-IV2 (eq 5.29), FT-III2, FT-III3, FT-IV2 (eq 5.30), FT-II3. Model FT-II3wasrejectedfrom list of bestmodels,becausetheoptimizedparametersof thismodelwereunrealisticandthemodeljust passedtheBartlett’s testdueto the large relative
INTRINSIC K INETICS OF THE GAS-SOLID FT AND WGS REACTIONS 159
Table5.8 FT kineticmodelscreening.
Model Sitebalance(eq) sr el (%) Rank Remarks
FT-I3 5.30 63.7 6FT-I4 5.30 65.9 9FT-II3 5.30 45.2 5FT-III2 5.29 30.0 2FT-III2 5.30 64.4 8FT-III3 5.29 30.9 3FT-III3 5.30 63.8 7FT-IV2 5.29 29.6 1FT-IV2 5.30 32.4 4FT-IV3 5.29,5.30 - - a Ò 0
FT-I3, FT-I4,FT-II3 with sitebalance5.29resultsin a Ó 0
variance. The site balancesof modelsFT-IV2 (eq 5.29) andFT-IV2 (eq 5.30) varyslightly only. Consequently, themodelwith thehighestrelativevariancewasrejected,i.e. FT-IV2 (eq5.30).
Four experimentswerefoundto beoutliersin thethreeremainingmodels(Runs:5, 17,20,23). Theremainingmodelswerefittedagainwith thereduceddatasetof 20experimentalreactionrates.Table5.10givestheoptimizedvaluesof theparametersinthesethreemodels:FT-III2, FT-III3, FT-IV2. Thethreeremainingkineticexpressions(FT-III2, FT-III3, andFT-IV2) areall basedonthecombinedenol/carbidemechanism.Themathematicalform of theequationsis verysimilar, indicatinga difficult discrim-inationprocedure.Figure5.2comparestheexperimentalandcalculatedreactionratesof thesethreemodels.
Kinetic expressionFT-IV2 is similar to severalliteraturemodels[7, 9, 10,22] foriron catalysts(seeTable5.5). In this model,theratedeterminingstepis a singlesitereactionbetweenundissociatedadsorbedCO andgaseousH2. However, theliteraturemodelsweredevelopedfrom experimentsin slurryphaseor packedbedreactors.Themajor differencebetweentheseliteraturemodelsandoptimizedmodelFT-IV2 is asignificantnumberof free sitesin the latter model. In our experiments,the catalystparticlesarelocatedin spinningbasketswith a small amountof high-boilinghydro-carbonspresentin thecatalystpores.
Kinetic expressionsFT-III2 andFT-III3 arealsoableto describeour experimentsaccurately. Thesemodelsarealsodevelopedfrom thecombinedenol/carbidemecha-
160 CHAPTER 5
R FT exp Ô . (mol kg -1 s Õ -1 )
Ö0.000 ×
0.002 ×
0.004 ×
0.006 ×
0.008 ×
0.010 ×
0.012 ×
R FT
mod
(m
ol k
g -1 s -1
)
0.000 ×0.002 ×0.004 ×0.006 ×0.008 ×0.010 ×0.012 ×
FT-III2 FT-III3 FT-IV2
-25 %
+25 %
cat
cat ØFigure5.2 Parity graphof experimentalandoptimizedFischer-Tropschreactionrates.
R WGS exp Ù (mol kg -1 s Ú -1 )
Û0.000 Ü
0.001 Ü
0.002 Ü
0.003 Ü
0.004 Ü
0.005 Ü
0.006 Ü
R W
GS
mod
(m
ol k
g -1 s -1
)
0.000 Ü0.001 Ü0.002 Ü0.003 Ü0.004 Ü0.005 Ü0.006 Ü
WGS-I5 WGS-II6
+ 25% Ý
- 25%
cat Þ
cat
Figure5.3 Parity graphof experimentalandoptimizedWGSreactionrates.
INTRINSIC K INETICS OF THE GAS-SOLID FT AND WGS REACTIONS 161
Table5.9 Bartlett’s testfor FT models1.H2 Ñ 2
c Ñ 2t
9 42Ë 2 15Ë 58 38Ë 2 14Ë 17 32Ë 6 12Ë 66 23Ë 6 11Ë 15 6 Ë 03 9 Ë 494 0 Ë 206 7 Ë 813 0 Ë 040 5 Ë 992 0 Ë 0037 3 Ë 841 ß 2
c : critical ß 2 accordingto Bartlett’s test[49]; ß 2t : tabulatedß 2 [51]
2 H : numberof modelsunderconsideration
nism: ratedeterminingstepsarethedualsitesurfacereactionbetweenundissociatedadsorbedCO anddissociatedH2 (FT-III2) andbetweenadsorbedformyl anddisso-ciatedH2 (FT-III3). Model FT-III2 is similar to the optimal equationof SarupandWojciechowski [14] for a precipitatedcobaltcatalystin a Berty reactor, whereasFT-III3 wasfoundto bethebestmodelby YatesandSatterfield[40] on cobaltmeasuredin a slurry reactor. The kinetic modelof SarupandWojciechowski [14] wasdevel-opedwith theassumptionthatthesitebalanceconsistsof freesites,adsorbedCOanddissociatedH2, while YatesandSatterfield[40] only includedCOinhibition.
The WGSreactionratewasoptimizedwith thekinetic expressionsin Table5.7.Dueto ahighdegreeof similarity betweenequationsWGS-I5andWGS-II6, therela-tivevariancesarealmostequal,25.0% and23.0%, respectively. TheBartlett’s testisunableto discriminatebetweenthesemodels.A parity plot betweentheexperimentalandmodelvaluesof the WGS reactionratesis shown in Figure5.3. ReactionrateexpressionWGS-II6 is similar to the optimal modelof Lox andFroment[5]. Bothmodelsassumethattherateof theWGSreactionis determinedby thereactionof ad-sorbedcarbonmonoxideandhydroxyl towardsa formateintermediate.Our modelassumesadsorptionof CO andwaterto bedominantin thesitebalance,whereasLoxand Froment[5] includedinhibition of hydroxyl speciesonly. The correspondingmodelparametersarealsogivenin Table5.10.
Both theexperimentalandthecalculatedratesof theFischer-Tropschandthewa-ter gasshift reactionarecomparedin Figures5.4- 5.5 at variousexperimentalcon-ditions. The calculatedratesstemfrom modelsFT-III2 andWGS-II6 with the input
162 CHAPTER 5
Table5.10 Finalestimatesfor theparametersof theFT andWGSkineticmodels.
Parameter Dimension Estimate
WGS-I5(sr el 21.0%)kÌ mol kg¶ 1 s¶ 1 MPa¶ 2 1.77 à 0.04K1 MPa¶ 1 2.10 à 0.04K3 MPa¶ 1 24.19à 3.14
WGS-II6 (sr el 21.5%)kÌ mol kg¶ 1 s¶ 1 MPa¶ 1Í 5 1.13 à 0.01K1 MPa¶ 1 2.78 à 0.04K3 MPa¶ 1 12.27à 0.94
FT-III2 (sr el 23.7%)k mol kg¶ 1 s¶ 1 MPa¶ 1Í 5 0.0488à 0.0049a MPa¶ 1 0.563à 0.094b MPa¶ 1 4.05 à 0.77
FT-III3 (sr el 22.4%)k mol kg¶ 1 s¶ 1 MPa¶ 2 0.0556à 0.0056a MPa¶ 1 0.125à 0.069b MPa¶ 1 7.00 à 0.87
FT-IV2 (sr el 22.7%)k mol kg¶ 1 s¶ 1 MPa¶ 2 0.0779à 0.0157a MPa¶ 1 0.536à 0.333b MPa¶ 1 32.27à 8.69
valuesof theH2/CO feedratioandtheflow rate, Î i nÏ"Ð 0 Ç W basedon stoichiometryandmassbalancesof thecomponentspresent(CO, CO2, H2, H2O). Theproductcompo-sition wasdeterminedfrom gaschromatographicanalysisof thegasandfrom liquidhydrocarbonproductsamples.Thevaluesof n andm weredeterminedfrom theprod-uct composition.In this study, n variedbetween2.86-5.04.The ratio of mÇ n variedbetween2.14-2.42.Theeffluentflow ratewasestimatedwith theaveragecontractionfactorcalculatedat mÇ n of 2.30. Sincethevariationof mÇ n with processconditionsis minor, thisassumptionseemsjustified.
Theeffect of theflow rateon theoverall rateandratesof thewatergasshift andFischer-Tropschreactionis demonstratedin Figure5.4a. As expected,the reactionratesincreasewith increasingspacevelocity. Thereis goodagreementbetweenthemodelcalculationsandtheexperimentalvalues.Overall conversionof synthesisgas,
INTRINSIC K INETICS OF THE GAS-SOLID FT AND WGS REACTIONS 163
R (
mol
kg-1
s-1)
cat
XC
O+
H2
Figure 5.4 Reactionratesfor theWGSandFT andtotal conversionof CO andH2 (a) andoverall conversionof synthesisgas(XCO á H2) versusspacevelocity (b). Symbolsareexper-imentalvalues.Linesaremodelpredictions(FT-III2 andWGS-II6).
164 CHAPTER 5
PCO (MPa) (feed)
0.0 0.5 1.0 1.50.000
0.005
0.010
0.015
0.020
0.025
0.030
-RCO+Hâ
2ã
RFT
RWGS
PH2ä (MPa) (feed)
0.5 1.0 1.5 2.0 2.5 3.00.000
0.005
0.010
0.015
0.020
0.025
0.030
RWGSåRFT
-RCO+Hâ
2ã
R(m
ol k
g-1
s-1
)ca
ta.æ b.
R(m
ol k
g-1
s-1
)ca
t
Figure 5.5 Reactionratesfor theWGSandFT andtotal conversionof CO andH2 versusreactantfeedpressures.Symbolsareexperimentalvalues.Linesaremodelpredictions(FT-III2 andWGS-II6). a: FeedpressurePCO= 0.8 MPa, T= 523 K, ç i nÏ Á W= 1.0 10¶ 3 kg¶ 1
cats¶ 1; b: FeedpressurePH2= 0.8MPa,T= 523K, ç i nÏ Á W= 1.010¶ 3 kg¶ 1
cat s¶ 1.
XCO á H2, at the sameconditionsis accuratelypredictedwith the optimizedkineticexpressionsanda CSTRreactormodel(seeFigure5.4b).
Theeffectof theindividual reactantpressures(PCO andPH2) in thefeedstreamisshown in Figures5.5a-b. Themodelsappearto predictthetrendsof varyingreactantpressuressatisfactory. Boththewatergasshift aswell astheFischer-Tropschreactionrateincreasewith increasingfeedpressureof CO (Figure5.5a). The waterpressuredecreaseswith increasingCO pressurecausingan increaseof the Fischer-Tropschreactionrate. Figure5.5b shows that the spacetime yield and the Fischer-Tropschreactionrateincreaseslightly andthendecreasemonotonically. This is causedby anincreaseof thehydrogenandwaterpressurein thereactorwith increasingfeedpres-sureof hydrogen.Wateris a stronginhibitor on thecatalystandreducesthereactionratesof thehydrocarbon-formingreactions.
5.5 Conclusions
Experimentsfor thekineticsof thehydrocarbonformationandwatergasshift reactionoveraniron catalystwereobtainedovera wide rangeof industriallyrelevantreactionconditions.A numberof rateequationswerederivedon thebasisof a detailedsetofpossiblereactionmechanisms.Thefollowing conclusionscanbemade:
INTRINSIC K INETICS OF THE GAS-SOLID FT AND WGS REACTIONS 165
1. Two differentsitesarepresenton iron catalysts.The iron carbidesareactivetowardshydrocarbonforming reactions,whereasmagnetite(Fe3O4) seemstobethemostactivesitefor thewatergasshift reaction.
2. Thereactionrateof theFischer-Tropschsynthesisis determinedby theforma-tion of themonomerspecies(methylene).Thebestmodelsassumethattheratedeterminingstepproceedsvia hydrogenationof associativeadsorbedCO.
3. Carbondioxideis formedby thewatergasshift reaction.Theratedeterminingstepis theformationof a formateintermediatespecies.
Simulationsusingthekineticmodelsderivedshow goodagreementwith bothex-perimentaldataandwith somekineticmodelsfrom literature.
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